Menu Close

Category: Vector

lim-x-0-1-x-1-1-x-1-x-1-1-3-1-

Question Number 171033 by cortano1 last updated on 06/Jun/22 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{{x}}\:\left[\:\sqrt[{\mathrm{3}}]{\frac{\mathrm{1}−\sqrt{\mathrm{1}−{x}}}{\:\sqrt{\mathrm{1}+{x}}−\mathrm{1}}\:}−\mathrm{1}\:\right]=? \\ $$ Commented by greougoury555 last updated on 07/Jun/22 $$\:\sqrt[{\mathrm{3}}]{\frac{\left(\mathrm{1}−\sqrt{\mathrm{1}−{x}}\right)\left(\mathrm{1}+\sqrt{\mathrm{1}−{x}}\right)}{\mathrm{1}+\sqrt{\mathrm{1}−{x}}}.\frac{\sqrt{\mathrm{1}+{x}}+\mathrm{1}}{\left(\sqrt{\mathrm{1}+{x}}−\mathrm{1}\right)\left(\sqrt{\mathrm{1}+{x}}+\mathrm{1}\right)}} \\ $$$$=\:\sqrt[{\mathrm{3}}]{\frac{{x}\left(\sqrt{\mathrm{1}+{x}}+\mathrm{1}\right)}{{x}\left(\mathrm{1}+\sqrt{\mathrm{1}−{x}}\right)}}\:=\:\sqrt[{\mathrm{3}}]{\frac{\sqrt{\mathrm{1}+{x}}+\mathrm{1}}{\mathrm{1}+\sqrt{\mathrm{1}−{x}}}\:} \\ $$$${L}=\underset{{x}\rightarrow\mathrm{0}}…

a-1-b-2-a-b-pi-3-a-b-

Question Number 170079 by depressiveshrek last updated on 16/May/22 $$\mid\overset{\rightarrow} {{a}}\mid=\mathrm{1} \\ $$$$\mid\overset{\rightarrow} {{b}}\mid=\mathrm{2} \\ $$$$\sphericalangle\left(\overset{\rightarrow} {{a}},\:\overset{\rightarrow} {{b}}\right)=\frac{\pi}{\mathrm{3}} \\ $$$$\mid\overset{\rightarrow} {{a}}+\overset{\rightarrow} {{b}}\mid=? \\ $$ Answered…

a-13-b-19-a-b-24-a-b-

Question Number 169885 by depressiveshrek last updated on 11/May/22 $$\mid\overset{\rightarrow} {{a}}\mid=\mathrm{13} \\ $$$$\mid\overset{\rightarrow} {{b}}\mid=\mathrm{19} \\ $$$$\mid\overset{\rightarrow} {{a}}+\overset{\rightarrow} {{b}}\mid=\mathrm{24} \\ $$$$\mid\overset{\rightarrow} {{a}}−\overset{\rightarrow} {{b}}\mid=? \\ $$ Answered…

cos-x-7-dx-

Question Number 169640 by MikeH last updated on 05/May/22 $$\int\mathrm{cos}\left({x}^{\mathrm{7}} \right){dx}\:= \\ $$ Commented by mkam last updated on 05/May/22 $$ \\ $$$$=\:\int\:\Sigma\:\left(−\mathrm{1}\right)^{{n}} \:×\:\frac{{x}^{\mathrm{14}{n}} }{\left(\mathrm{2}{n}\right)!}\:{dx}\:=\:\Sigma\:\frac{\left(−\mathrm{1}\right)^{{n}}…

check-that-the-function-u-x-t-exp-n-2-2-pi-2-L-2-t-sin-npix-L-n-1-2-satisfy-the-heat-equation-heat-equation-2-2-u-x-2-u-t-0-lt-x-lt-L-

Question Number 168977 by MikeH last updated on 23/Apr/22 $$\mathrm{check}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function} \\ $$$${u}\left({x},{t}\right)\:=\:\mathrm{exp}\left\{−\frac{{n}^{\mathrm{2}} \alpha^{\mathrm{2}} \pi^{\mathrm{2}} }{{L}^{\mathrm{2}} }{t}\right\}\:\mathrm{sin}\frac{{n}\pi{x}}{{L}} \\ $$$${n}\:=\:\mathrm{1},\mathrm{2},…\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{heat}\:\mathrm{equation} \\ $$$$\boldsymbol{\mathrm{heat}}\:\boldsymbol{\mathrm{equation}} \\ $$$$\alpha^{\mathrm{2}} \frac{\partial^{\mathrm{2}} {u}}{\partial{x}^{\mathrm{2}} }\:=\:\frac{\partial{u}}{\partial{t}},\:\mathrm{0}\:<\:{x}\:<\:{L}…

pi-4-pi-2-ln-ln-tan-x-dx-

Question Number 103190 by bemath last updated on 13/Jul/20 $$\underset{\pi/\mathrm{4}} {\overset{\pi/\mathrm{2}} {\int}}\mathrm{ln}\left(\mathrm{ln}\left(\mathrm{tan}\:{x}\right)\right)\:{dx}\: \\ $$ Answered by abdomathmax last updated on 13/Jul/20 $$\mathrm{ln}\left(\mathrm{tanx}\right)\:=\mathrm{t}\:\Rightarrow\:\mathrm{I}\:=\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{ln}\left(\mathrm{ln}\left(\mathrm{tanx}\right)\right)\mathrm{dx} \\…

Question-168121

Question Number 168121 by rexford last updated on 03/Apr/22 Answered by FelipeLz last updated on 04/Apr/22 $$\overset{\rightarrow} {{r}}\:=\:\left({a},\:{b},\:{c}\right) \\ $$$$\left.\begin{matrix}{\overset{\rightarrow} {{r}}\centerdot\hat {\imath}\:=\:{a}}\\{\overset{\rightarrow} {{r}}\centerdot\hat {\jmath}\:=\:{b}}\\{\overset{\rightarrow} {{r}}\centerdot\hat…